U.S. patent application number 14/525155 was filed with the patent office on 2015-03-12 for system for weighing individual micro- and nano- sized particles.
This patent application is currently assigned to Purdue Research Foundation. The applicant listed for this patent is Purdue Research Foundation. Invention is credited to Bin-Da Chan, Kutay Icoz, Cagri Abdullah Savran.
Application Number | 20150068309 14/525155 |
Document ID | / |
Family ID | 61280579 |
Filed Date | 2015-03-12 |
United States Patent
Application |
20150068309 |
Kind Code |
A1 |
Savran; Cagri Abdullah ; et
al. |
March 12, 2015 |
SYSTEM FOR WEIGHING INDIVIDUAL MICRO- AND NANO- SIZED PARTICLES
Abstract
A device for weighing micro- and nano-sized particles. The
device includes a base portion, an oscillator coupled to the base
portion and configured to vibrate the base portion, a first
cantilevered beam coupled to the base portion, a second
cantilevered beam coupled to the base portion, a first plurality of
fingers coupled to the first cantilevered beam near the tip
inwardly pointing toward the second cantilevered beam, and a second
plurality of fingers coupled to the second cantilevered beam near
the tip inwardly pointing toward the first cantilevered beam.
Inventors: |
Savran; Cagri Abdullah;
(West Lafayette, IN) ; Chan; Bin-Da; (West
Lafayette, IN) ; Icoz; Kutay; (Kayseri, TR) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Purdue Research Foundation |
West Lafayette |
IN |
US |
|
|
Assignee: |
Purdue Research Foundation
West Lafayette
IN
|
Family ID: |
61280579 |
Appl. No.: |
14/525155 |
Filed: |
October 27, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61876743 |
Sep 11, 2013 |
|
|
|
Current U.S.
Class: |
73/580 |
Current CPC
Class: |
G01G 3/165 20130101;
G01G 3/16 20130101 |
Class at
Publication: |
73/580 |
International
Class: |
G01G 9/00 20060101
G01G009/00; G01G 17/00 20060101 G01G017/00 |
Goverment Interests
GOVERNMENT SUPPORT CLAUSE
[0002] This invention was made with government support under Grant
No. 0925417 awarded by the National Science Foundation. The
government has certain rights in the invention.
Claims
1. A device for weighing micro- and nano-sized particles,
comprising: a base portion; an oscillator coupled to the base
portion configured to vibrate the base portion; a first
cantilevered beam coupled to the base portion at a proximal end and
having a tip portion at a distal end; a second cantilevered beam
coupled to the base portion at a proximal end and having a tip
portion at a distal end; a first plurality of fingers coupled to
the first cantilevered beam near the tip inwardly pointing toward
the second cantilevered beam; and a second plurality of fingers
coupled to the second cantilevered beam near the tip inwardly
pointing toward the first cantilevered beam, the first plurality of
fingers interdigitating with the second plurality of fingers such
that the first cantilevered beam and the second cantilevered beam
can oscillate independent of each other, and where the
interdigitating fingers separated by gaps that are sufficiently
small for light reflected from the interdigitating fingers during
oscillation of the first and second cantilevered beams to form a
diffraction pattern.
2. The device of claim 1, the tip of the first cantilevered beam
includes a first retaining feature configured to maintain position
of a particle placed thereon for weighing.
3. The device of claim 2, the tip of the second cantilevered beam
includes a second retaining feature configured to maintain position
of a reference weight placed thereon for weighing the particle.
4. The device of claim 1, the first and second cantilevered beams
are silicon-based.
5. The device of claim 1, each cantilevered beam has a length of
between about 50 .mu.m to 500 .mu.m and a width outside of the tip
portion of between about 10 .mu.m to 100 .mu.m.
6. The device of claim 5, each tip portion has a width of between
about 10 .mu.m to 100 .mu.m.
7. The device of claim 6, each of the fingers has a width of
between about 2 to 5 .mu.m and a length of between about 10 .mu.m
to 100 .mu.m and the gap is between about 1 .mu.m to 5 .mu.m.
8. A system for weighting micro- and nano sized particles,
comprising: a resonator, the resonator comprising: a base portion,
an oscillator configured to provide mechanical vibration according
to a selective sweep of frequencies to the base portion; a first
cantilevered beam coupled to the base portion at a proximal end and
having a tip portion at a distal end, a second cantilevered beam
coupled to the base portion at a proximal end and having a tip
portion at a distal end, a first plurality of fingers coupled to
the first cantilevered beam near the tip inwardly pointing toward
the second cantilevered beam, and a second plurality of fingers
coupled to the second cantilevered beam near the tip inwardly
pointing toward the first cantilevered beam, the first plurality of
fingers interdigitating with the second plurality of fingers such
that the first cantilevered beam and the second cantilevered beam
can oscillate independent of each other, and where the
interdigitating fingers separated by gaps that are sufficiently
small for light reflected from the interdigitating fingers during
oscillation of the first and second cantilevered beams to form a
diffraction pattern; a light source positioned proximate to the
resonator and configured to shine light on the interdigitating
fingers; and at least one optical detector positioned proximate to
the resonator to measure light intensity of at least one of the
modes of the diffraction pattern.
9. The system of claim 8, the at least one mode is the 0.sup.th
mode.
10. The system of claim 8, the light source is a laser.
11. The system of claim 8, the tip of the first cantilevered beam
includes a first retaining feature configured to maintain position
of a particle placed thereon for weighing.
12. The system of claim 11, the tip of the second cantilevered beam
includes a second retaining feature configured to maintain position
of a reference weight placed thereon for weighing the particle.
13. The system of claim 8, the first and second cantilevered beams
are silicon-based.
14. A method for measuring mass of a micro- and nano-sized particle
comprising: placing the micro- or nano-sized particle on a
resonator, the resonator comprising: a base portion, an oscillator
configured to provide mechanical vibration according to a selective
sweep of frequencies to the base portion; a first cantilevered beam
coupled to the base portion at a proximal end and having a tip
portion at a distal end, a second cantilevered beam coupled to the
base portion at a proximal end and having a tip portion at a distal
end, a first plurality of fingers coupled to the first cantilevered
beam near the tip inwardly pointing toward the second cantilevered
beam, and a second plurality of fingers coupled to the second
cantilevered beam near the tip inwardly pointing toward the first
cantilevered beam, the first plurality of fingers interdigitating
with the second plurality of fingers such that the first
cantilevered beam and the second cantilevered beam can oscillate
independent of each other, and where the interdigitating fingers
separated by gaps that are sufficiently small for light reflected
from the interdigitating fingers during oscillation of the first
and second cantilevered beams to form a diffraction pattern;
energizing the oscillator at a selective frequency thereby causing
mechanical vibration in the first and second cantilevered arms;
directing a light beam from a light source onto the interdigitating
fingers; sensing intensity of light of the reflected diffraction
pattern by at least one photodetector positioned about at least one
of the modes; varying the frequency by sweeping a range of
frequencies; and correlating the sensed intensity to mass to
thereby determine the mass of the micro- or nano-sized
particle.
15. The method of claim 14, the energizing further comprising:
varying the frequency by sweeping a range of frequencies.
16. The method of claim 15, further comprising: determining a
resonance frequency differential between the resonance frequency of
each of the cantilevered beams based on the sensed intensity.
17. The method of claim 14, the at least one mode is the 0.sup.th
mode.
18. The method of claim 14, the light source is a laser.
19. The method of claim 14, the first and second cantilevered beams
are silicon-based.
20. The method of claim 14, further comprising: placing a reference
weight on the resonator, where the micro- or nano-sized particle is
placed on the first cantilevered beam and the reference weight is
placed on the second cantilevered beam.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present U.S. patent application is related to and claims
the priority benefit of U.S. Provisional Patent Application Ser.
No. 61/895,734, filed Oct. 25, 2013, the contents of which are
hereby incorporated by reference in their entirety into the present
disclosure.
TECHNICAL FIELD
[0003] The present application relates to weighting systems and
particularly to a micro- and nano-scale weighting system.
BACKGROUND
[0004] This section introduces aspects that may help facilitate a
better understanding of the disclosure. Accordingly, these
statements are to be read in this light and are not to be
understood as admissions about what is or is not prior art.
[0005] The need to weigh micro-sized particles has become
prevalent. Several approaches have been used to accomplish such
weighing. One approach is based on cantilever-based
micro/nano-sensors which have been used extensively over the past
decade to detect a wide variety of entities including
bio-molecules, chemicals, viruses and cells. These sensors have
been used both in static (i.e. stress sensing) and dynamic (i.e.
resonating) modes. The latter mode reveals the mass of the target
entity by measuring changes in the resonance frequency of the
cantilever.
[0006] Current strategies of weight measurement using cantilevers
mostly depend upon probabilistic attachment of the targets on the
cantilever surface. For example, resonators have been used to weigh
single bacteria and viruses that bind to sensor surfaces both
specifically and nonspecifically. The embodiments provided in the
prior art have used suspended micro-channel resonators to measure
bio-molecules and single nano-particles by flowing the target
entities through the inner micro-channel of a cantilever.
[0007] The nature of the cantilever-based systems of the prior art,
however, render them susceptible to error. Furthermore, the
probabilistic nature of target attachment reduces the repeatability
of measurements of a micro-particle specimen array. In addition,
when one relies on probabilistic attachment of target entities,
this approach makes it challenging to weigh an individual particle
specifically selected by the user from a pool of other particles
whose weights are not desired.
[0008] There is, therefore an unmet need for a novel approach to
weigh individual micro/nano-sized particles of varying sizes while
reducing errors associated with methodologies used in the prior
art.
SUMMARY
[0009] A device for weighing micro- and nano-sized particles is
disclosed. The device includes a base portion and an oscillator
which is coupled to the base portion and is configured to vibrate
the base portion. The device also includes a first cantilevered
beam which is coupled to the base portion at a proximal end and
having a tip portion at a distal end, and a second cantilevered
beam coupled to the base portion at a proximal end and having a tip
portion at a distal end. The device further includes a first
plurality of fingers coupled to the first cantilevered beam near
the tip inwardly pointing toward the second cantilevered beam, and
a second plurality of fingers coupled to the second cantilevered
beam near the tip inwardly pointing toward the first cantilevered
beam. The first plurality of fingers interdigitating with the
second plurality of fingers such that the first cantilevered beam
and the second cantilevered beam can oscillate independent of each
other. The interdigitating fingers are separated by gaps that are
sufficiently small for light reflected from the interdigitating
fingers during oscillation of the first and second cantilevered
beams to form a diffraction pattern.
[0010] A system for weighting micro- and nano-sized particles is
also disclosed. The system includes a resonator. The resonator
includes a base portion and an oscillator which is coupled to the
base portion and is configured to vibrate the base portion. The
resonator also includes a first cantilevered beam which is coupled
to the base portion at a proximal end and having a tip portion at a
distal end, and a second cantilevered beam coupled to the base
portion at a proximal end and having a tip portion at a distal end.
The resonator further includes a first plurality of fingers coupled
to the first cantilevered beam near the tip inwardly pointing
toward the second cantilevered beam, and a second plurality of
fingers coupled to the second cantilevered beam near the tip
inwardly pointing toward the first cantilevered beam. The first
plurality of fingers interdigitating with the second plurality of
fingers such that the first cantilevered beam and the second
cantilevered beam can oscillate independent of each other. The
interdigitating fingers are separated by gaps that are sufficiently
small for light reflected from the interdigitating fingers during
oscillation of the first and second cantilevered beams to form a
diffraction pattern. The system also includes a light source
positioned proximate to the resonator and is configured to shine
light on the interdigitating fingers. The system also includes at
least one optical detector that is positioned proximate to the
resonator to measure light intensity of at least one of the modes
of the diffraction pattern.
[0011] A method for measuring mass of a micro- and nano-sized
particles is disclosed. The method includes placing the micro- or
nano-sized particle on a resonator. The resonator includes a base
portion and an oscillator which is coupled to the base portion and
is configured to vibrate the base portion. The resonator also
includes a first cantilevered beam which is coupled to the base
portion at a proximal end and having a tip portion at a distal end,
and a second cantilevered beam coupled to the base portion at a
proximal end and having a tip portion at a distal end. The
resonator further includes a first plurality of fingers coupled to
the first cantilevered beam near the tip inwardly pointing toward
the second cantilevered beam, and a second plurality of fingers
coupled to the second cantilevered beam near the tip inwardly
pointing toward the first cantilevered beam. The first plurality of
fingers interdigitating with the second plurality of fingers such
that the first cantilevered beam and the second cantilevered beam
can oscillate independent of each other. The interdigitating
fingers are separated by gaps that are sufficiently small for light
reflected from the interdigitating fingers during oscillation of
the first and second cantilevered beams to form a diffraction
pattern. The method also includes energizing the oscillator at a
selective frequency thereby causing mechanical vibration in the
first and second cantilevered arms. The method further includes
directing a light beam from a light source onto the interdigitating
fingers. In addition, the method includes sensing intensity of
light of the reflected diffraction pattern by at least one
photodetector positioned about at least one of the modes and
varying the frequency by sweeping a range of frequencies. The
method also includes correlating the sensed intensity to mass to
thereby determine the mass of the micro- or nano-sized
particle.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] The above and other objects, features, and advantages of the
present invention will become more apparent when taken in
conjunction with the following description and drawings wherein
identical reference numerals have been used, where possible, to
designate identical features that are common to the figures, and
wherein:
[0013] FIG. 1 is a perspective view of a system for weighing micro-
and nano-sized particles incorporating a resonator as described
herein.
[0014] FIG. 2 is a top view of the resonator of FIG. 1 depicting a
plurality of interdigitating fingers.
[0015] FIG. 2a is an enlarged view of two adjacent interdigitated
fingers of FIG. 2.
[0016] FIG. 3 is a graph of frequency shift as a function of the
position of a target particle on a cantilevered arm of the
resonator shown in FIG. 1.
[0017] FIG. 4 is a graph of frequency differential between an
unloaded reference arm and loaded sensor arms of the resonator and
system shown in FIG. 1.
[0018] FIG. 5 is a graph showing the standard deviation in measured
frequency shift as a function of excitation voltage and loading of
the resonator shown in FIG. 1.
[0019] FIG. 6 is a scanning electron micrograph (SEM) of two stem
cell spheres mounted on the cantilevered beams of the resonator as
shown in FIG. 1.
[0020] FIG. 7 is a graph of the frequency spectrum showing the
comparative weighing of the two stem cell spheres depicted in FIG.
6.
[0021] FIG. 8 is a micrograph of the resonator of FIG. 1 shown with
a spore cluster mounted on the sensor beam and a reference bead
mounted on the reference beam, together with an inset view showing
an SEM image of the spore cluster.
[0022] FIG. 9 is a graph of the change in differential frequency
with increasing humidity for the experimental set-up shown in FIG.
8.
[0023] FIG. 10 is an SEM image of the contents of a dried pond
water sample.
[0024] FIG. 11 is an SEM image of a diatom obtained from the sample
shown in FIG. 10, with the diatom mounted on the sensor beam of a
resonator as shown in FIG. 1, with an inset of the diatom on the
end of the beam.
[0025] The attached drawings are for purposes of illustration and
are not necessarily to scale.
DETAILED DESCRIPTION
[0026] For the purposes of promoting an understanding of the
principles of the present disclosure, reference will now be made to
the embodiments illustrated in the drawings, and specific language
will be used to describe the same. It will nevertheless be
understood that no limitation of the scope of this disclosure is
thereby intended.
[0027] The present disclosure describes a system that allows
weighing a wide variety of individual micro- and nano-particles by
placing them onto a resonator. A single target entity that is
selected under a microscope is grabbed by a micro-manipulator and
the entity is placed on the tip of a sensor beam of the cantilever
for weighing. The particle weight is determined using optical
diffraction modes, which permits highly accurate weight
measurements as well as measurement of relative weight differences
between particles.
[0028] In one feature, the system 1 includes a resonator 10, as
illustrated in FIGS. 1-2, a light source 30, an optical detector
array 40, and a function generator 52. The light source 30 is
configured to shine light 32 to the resonator 10. Reflected light
34 reflects from the resonator and strikes the optical detector
array 40 according to a diffraction pattern. The diffraction
pattern includes spots or "modes", including 0.sup.th mode. The
optical detector array 40 includes at least one optical detector 36
positioned to sense the intensity of one of the modes, e.g., the
0.sup.th mode.
[0029] The resonator 10 includes at least two adjacent beams 12a,
12b cantilevered from a base 14. The base 14 is attached to a
piezoelectric shaker 50, but can be any electromechanically
activated vibration mechanism. In one use of the resonator 10, one
of the beams 12b serves as an inherent reference operable to
suppress noise and other disturbances that affect both cantilevers
similarly. The other beam 12a serves as the beam for the target
particle. The beams 12a, 12b are preferably identically sized and
shaped so that no or only minimal adjustments or calibrations are
required to ensure accurate results. The beams may be formed in
various geometries, but the rectangular geometry depicted in FIGS.
1-2 may be more suitable for fabrication purposes. Each beam
includes a cantilevered arm 16 with the free end defining an
enlarged support surface 18 for supporting a target particle. The
support surface is enlarged to provide ample area for placement of
the target particle by a micro-manipulator.
[0030] Each beam 12a and 12b includes two segments: arms 16a and
16b; and support surfaces 18a and 18b (also referred to as tip
portions), respectively. In one important feature, each
cantilevered beam includes a plurality of laterally-directed
fingers 20a, 20b. As seen in the figures, the fingers are
interdigitated so that light illuminating the beams produces a
diffraction pattern, as described herein. The resonator may be
fabricated using known micro-fabrication techniques, such as
photolithography, etching or other known techniques. In the
embodiment shown in the figures, the cantilevered beams each have a
length of 50 .mu.m to 500 .mu.m or more narrowly between 200 .mu.m
to 300 .mu.m; a width at the arms 16a and 16b of between about 10
.mu.m to 100 .mu.m and a width at the support surface 18 of between
about 10 .mu.m to 100 .mu.m, or more narrowly between 35 .mu.m to
85 .mu.m, not including the interdigitated fingers. The fingers
20a, 20b, depicted in FIG. 2a, each have a width 20w of 2 to 5
.mu.m and a length 20l of about 10 .mu.m to 100 .mu.m or more
narrowly 40 .mu.m to 60 .mu.m and can range between 4 to 15 in
number for each set of fingers with a gap 20g of 1 .mu.m to 5
.mu.m. The beams 12a and 12b each have a thickness of about 10 nm
to 2 .mu.m, or more narrowly between 500 nm to 1 .mu.m.
[0031] The resonator may be formed as a silicon-rich silicon
nitride layer. The fingers 20a and 20b may be coated with a thin
layer of gold to improve reflectivity.
[0032] The system 1 includes the light source 30, e.g., a laser
(NEWPORT R-30091, 5 mW, for example), that is oriented to
illuminate the fingers, as shown in FIG. 1. The photo diode array
40 (THORLABS DET110, for example) is arranged to measure the
intensity of the 0.sup.th mode of the reflected diffraction
pattern. By analyzing the intensity change of the reflected
diffraction mode, the resonance frequencies of both cantilevers can
be deduced. The resonator 10 further includes the piezoelectric
shaker 50 (THORLABS AE0203D04F, for example) that is attached to
the bottom of the base 14 for excitation of the resonator. The
oscillation amplitude and frequency of the shaker are controlled by
a function generator 52 (TEKTRONIX AFG3102, for example). A lock-in
amplifier (Stanford Research Systems SR830) is used to record the
signal at the excitation frequency.
[0033] Changes in resonance frequency are measured to resolve the
loading upon the cantilever, which is expressed by:
f = 1 2 .pi. K 0.243 M + m [ 19 ] , Equation 1 ##EQU00001## [0034]
where M is the effective mass of the cantilever, [0035] m is the
mass of the load, and [0036] K is the effective stiffness of the
cantilever. Accordingly, the difference between the resonance
frequencies of the reference and the sensor cantilevers are
expressed by the following equation:
[0036] .DELTA. f = 1 2 .pi. ( K 0.243 M + m r - K 0.243 M + m ) ,
Equation 2 ##EQU00002## [0037] where m.sub.r is the added load on
the reference cantilever, and [0038] m is the added mass on the
sensor cantilever. Since the cantilevers are not perfectly
rectangular, K and M can be determined by combining finite element
simulations with experiments. In one experiment, the effective
density of a cantilever beam was taken as 3.65 g/cm.sup.3 by
averaging a 20 nm thick gold layer with a density of 19.3
g/cm.sup.3 and a 480 nm of silicon-rich silicon nitride layer with
a density of 3 g/cm.sup.3. The Young's modulus was then estimated
to be 182.2 GPa by matching the resonance frequency predicted by
the finite element simulation with that observed experimentally
(6642 Hz). Next, the value for K was determined to be 0.0195 N/m
using a finite element simulation by applying a vertical point
force at the tip and observing the resulting tip deflection.
Finally, M was determined to be 46.08 nano-gram by substituting K
into the Equation 1. With the constants of the above equations
determined, the only variables are the masses of the target and
reference particles, m and m.sub.r.
[0039] For maximum measurement sensitivity the load or target is
preferably exactly at the tip of the cantilever. Hence, the
micromanipulator here also serves the purpose of placing the target
as close to the tip of the cantilever as possible, improving the
accuracy of mass measurements. Nevertheless, the effect of loading
location on the resonance frequency can be addressed in the
weight/mass measurement process. An element analysis can be used to
demonstrate the relationship between the resonance frequency and
the location of the center of mass of the target entity T
positioned on the enlarged surface 18 as depicted in FIG. 3. The
variation of the resonance frequency shift with different loading
masses and locations on the sensor arm is demonstrated in the graph
of FIG. 3. The solid line curve corresponds to an empty reference
cantilever 12b and the data points represent the results of the
finite element simulation for different target entity positions
from the free end or tip of the arm 12a. For improved accuracy in
determining the mass, the location of the target entity can be
determined using calibrated brightfield microscopy and a
corresponding frequency shift vs. mass curve can be generated using
finite element analysis.
[0040] The graph of FIG. 4 shows experimental results of frequency
response of the system when one of the cantilevers (the sensor arm
12a) is loaded with three different masses. In each experiment, an
individual polystyrene bead (Spherotech) with a different mass was
placed on the enlarged surface 18 of the sensor arm 12a for
weighing. Prior to the placement, the micromanipulator was used to
dip the bottom of the bead in a small amount of grease. It has been
found that the grease can efficiently improve the adhesion between
the target particles and the cantilever surface but has negligible
mass (.about.70 pico-gram) in comparison with the particles being
weighed. Alternatively, the grease can be placed directly on the
cantilever surface before placing the target entities, in which
case the impact of the grease on the system frequency response can
be directly accounted for before the measurements. In FIG. 4, the
frequencies corresponding to the two peaks represent the resonance
frequencies of the sensor arm 12a (low frequency peak) and the
reference arm 12b (high frequency peak). Initially, since both
cantilevers are empty, no significant frequency separation occurs
and two resonance peaks overlap with each other, as reflected in
the lower curve in the graph of FIG. 4. As the load on the sensor
arm increases, the resonance peak corresponding to the sensor arm
shifts to the left, while the resonance peak of the reference arm
remains fixed, so the two resonance frequencies separate. The 9.3
nano-gram bead (middle curve) and the 46.5 nano-gram bead (upper
curve) were located 11.6 .mu.m and 12.2 .mu.m away from the tip of
the cantilever, respectively. The resonance frequency of the
reference arm is unchanged because there is no significant change
of mass on the reference arm.
[0041] The mass of the load on the sensor arm can be derived
readily from the frequency separation between the two peaks with a
single measurement. In particular, the frequency shift value can be
applied to Equation 2 to solve for the value m corresponding to the
mass of the target particle T. In the case where no reference mass
is added to the reference cantilevered arm 12b the value for
m.sub.r is zero. It is further contemplated that the system can be
used to directly determine the differential mass between two
particles by loading both cantilevers (instead of leaving the
reference arm empty). In this case, the reference arm frequency
will also shift to the left in FIG. 4 from the unloaded reference
frequency. In Equation 2, the value for m.sub.r will be non-zero,
corresponding to the mass of the second particle positioned on the
arm 12b. Alternatively, instead of using the Equations 1 and 2, one
can prefer to determine the added masses by matching the
experimentally observed resonance frequencies with those observed
in a finite element simulation of the cantilevered system bearing
loads with the same shape and location as determined
microscopically, and varying the value of the masses in simulation
until the resulting resonance frequency in the simulation matches
those observed experimentally.
[0042] The system shown in FIG. 2, and particularly the resonator
10 shown in FIG. 1, provide repeatable resonance frequency
measurements, and consequently repeatable weight/mass measurements
for micro- and nano-particles. In one verification experiment, the
sensing cantilever arm 12a was loaded with an individual
polystyrene bead with a known mass and the peak-to-peak excitation
voltage to the piezoelectric shaker 50 was varied. Two different
beads with different masses (9.3 nano-gram and 46.5 nano-gram) were
used and each experiment was repeated five times at each excitation
voltage. The standard deviation of the measured resonance frequency
was then calculated. The results shown in the graph of FIG. 5
indicate that the repeatability of the measurements improves both
with mass loading and with excitation voltage. As reflected in the
graph, increasing the load at each excitation voltage resulted in a
decrease in standard deviation, with the decrease being more
dramatic at the higher voltages. As also shown in the graph, as the
excitation voltage is increased the standard deviation decreases
for each loading condition, with the standard deviation at the
highest voltage being about one-third the standard deviation at the
lowest voltage. This reduction in standard deviation is due in part
to an increase in mass improving the quality factor of the
cantilever, and an increase in external excitation improving the
signal-to-noise ratio of the measurement. Hence, in some
experiments, in order to reduce the standard deviation of the
measured frequency shift, it may be preferable to provide a
reference bead of known mass on the reference arm 12b instead of
leaving it unloaded. With this modification, the potential error in
the resonance frequency can be as low as 1 Hz, which corresponds to
about 3 pico-gram with the cantilever mass and stiffness values
described above (as calculated using Equation 2).
[0043] The effect of other uncertainties on the accuracy of the
mass measurement has been investigated. One uncertainty arises from
the fabrication of a given wafer forming the resonator 10 may
result in wafer dimensions that vary between the two cantilevered
arms 12a, 12B. For instance, in one example a change in thickness
due to non-uniformity of nitride deposition was measured as 8 nm
over a distance of 3 inches on a photolithography wafer, which for
a 500 nm-thick film, could alter the stiffness of a cantilever by
4.9% (cubic dependence on thickness) and its mass by 1.6% (linear
dependence on thickness). According to Equation 1, the combined
effect of this stiffness and mass difference on the natural
frequency of a cantilevered arm (with nominal M of 46.08 nano-gram
and K of 0.0195 N/m) would be about 106 Hz. However, due to the
differential nature of the system as shown in Equation 2, for small
loads up to 2 nano-gram, this effect is suppressed to below 1 Hz
Even for a 10 nano-gram load, the uncertainty would be only about
11 Hz corresponding to a potential error of about 100
pico-gram).
[0044] In another experiment, two cantilevers that were 2 inches
apart on a photolithography wafer were found to differ in length by
as much as 1 .mu.m (possibly due to alignment errors during
photolithography). For a 250 .mu.m long cantilever, the effect of
this uncertainty on stiffness can be about 1.2%, and on mass about
0.4%, with the combined effect producing a 53 Hz uncertainty on
resonance frequency. However, in a differential system (according
to Equation 2) while measuring small loads (<290 pico-gram),
uncertainty in length results in no detectable error in resonance
frequency shift. For a 10 nano-gram load, the uncertainty would be
19 Hz (about 200 pico-gram). In practice however, these errors can
be mitigated by measuring the dimensions of the particular
cantilevers with high accuracy using scanning electron microscopy
(SEM) and determining the related M and K before the measurement.
For example, a 2 nm uncertainty in measuring thickness in SEM would
result in no detectable errors in measuring loads up to 4.7
nano-gram, a 24 pico-gram error in measuring a 10 nano-gram load
and a 1.5 nano-gram error in measuring a 100 nano-gram load. A 2 nm
uncertainty in 250 .mu.m nominal length would result in no
detectable error in resonance frequency. Note that the above
uncertainty analyses assumed that the reference cantilever is
empty. Hence for a differential system, loading the reference
cantilever with a mass similar to that on the sensing cantilever
can further mitigate the effects of uncertainties. Another
experiment evaluated the frequency uncertainty as a function of the
location of the target particle or load on the cantilevered arms.
An analysis similar to that shown in the graph of FIG. 3 suggests
that a 200 nm uncertainty in assessing the location of the load
(the limit of a typical brightfield microscope) would result in a
23 pico-gram uncertainty in the measured mass of a 10 nano-gram
particle. This uncertainty is less than 3 pico-gram while measuring
particles that weigh 1 nano-gram or less. For many applications,
this uncertainty can be further mitigated by measuring the location
of the target particle or load using SEM.
Weighing of Individual Stem Cell Spheres
[0045] In one procedure, the system was used to weigh individual
stem cell spheres. Currently, stem cells are of interest because of
their capacity for organ replenishment and for their potential role
in cancer initiation and progression. Stem cells form multiple
spheres in soft agar. These spheres are usually not analyzed
individually but en masse. With the system disclosed herein an
individual stem cell sphere can be extracted from culture medium
and weighed. One experiment was conducted with adolescent male
murine prostate stem cell spheres that were cultured for 10 days.
The cell spheres were fixed by formalin, followed by dehydration
using ethanol. Then, the stem cell spheres were left to dry on a
glass surface for subsequent testing steps. FIG. 6 illustrates the
SEM image of two stem cell spheres placed on different cantilevers
for weighing. One of the cantilevers was loaded with a larger stem
cell sphere located 14.2 .mu.m away from the cantilever tip, while
the smaller sphere was located 9.8 .mu.m away from the cantilever
tip. The frequency response of the loaded resonator, as shown in
FIG. 7, show a left peak and the right peak of the frequency
spectrum illustrate the resonance frequencies corresponding to the
cantilevers loaded with larger and smaller spheres, respectively.
The difference in the masses of both cell spheres is derived from
the differential frequency of 1663 Hz as 88.2 nano-gram with the
mass of the big cell sphere being 114 nano-gram and small sphere
being 25.8 nano-gram. The ability to easily compare two individual
stem cell spheres in terms of mass could offer interesting
possibilities in understanding their biology and their response to
various treatments.
Humidity Response of Bacillus Subtilis Spores
[0046] In another procedure the system was used to assess the
response of Bacillus subtilis spores to environmental stimuli.
These spores can absorb water, and dehydrate when heated. By
weighing the spores at different humidity levels, the amount of
water absorbed by the spores can be measured. The experiment
started by collecting spore clusters using a micromanipulator.
After the spores were dried out on a glass surface, the
micromanipulator was employed to tenderly pile up the spores. The
multilayered coat structure of each spore renders it as one of the
most durable cell types so that the spores remain intact after
being grouped. After collecting sufficient spores, the cluster of
spores was picked up and placed on the tip of the cantilever arm,
which had been pre-paved with a thin layer of grease to prevent the
spore cluster from flying away. This particular cantilever pair is
slightly different from the one used in the previously described
experiment hence the effective stiffness and the effective mass
were determined again as 0.0187 N/m and 45.6 nano-gram,
respectively. As seen in photomicrograph of FIG. 8, the sensor arm
12a of the cantilever resonator was loaded with a cluster of B.
subtilis spores, and the reference arm 12b was loaded with a
reference bead. The experiment took place in a closed space to
facilitate humidity control.
[0047] The resulting relationship between humidity change and mass
is shown in the graph of FIG. 9. The initial frequency shift value
is deliberately set to 0 for clarity. The initial mass of the spore
cluster was 18.8 nano-gram, which varied with relative humidity.
The mass increased from 18.8 nano-gram to 23.2 nano-gram as the
relative humidity increased from 36% to 92%. The 23.5% increase in
the spore mass is in accordance with a previous study. The effect
of humidity on the cantilevers themselves is suppressed by the
inherently differential detection. Consequently, only the water
adsorbed in the spores is measured.
Weighing of Diatoms from Pond Water
[0048] In a further example of the versatility of the system and
resonator disclosed herein, the system was used to weigh individual
diatom algae. Diatoms are unicellular algae that are widely
observed in aquatic environments. They have been extensively
studied in various fields including ecology, bioengineering,
medicine, and nanotechnology. Due to their special features (such
as amorphous silica skeletons, uniform nano-porous structures,
chemical inertness, and versatile forms and sizes) researchers have
proposed multiple applications of diatoms such as in biophotonics,
microfluidics, nanofabrication, gel filtration, and drug delivery,
The ability of the system disclosed herein to individually pick and
weigh single diatoms could provide new insight into their
characterization and their use as biotechnological tools. To
measure the mass of diatom particles, a cantilever arm with
circular head shape was used to weigh single diatom cells, as shown
in the photo micrograph of FIG. 11. The effective stiffness of this
particular cantilever pair was 0.0188 N/m and the effective mass
was calculated as 54.2 nano-gram. In the experiment, a drop of
outdoor pond water that contained large amounts of diverse
microorganisms including bacteria, algae, and protozoa, was first
left to dry in air on a glass slide.
[0049] FIG. 10 shows a spot on the glass slide with numerous
micro-particles, a pennate-type diatom and other microorganisms. A
single diatom was extracted using a micromanipulator and place it
at the tip of the sensor cantilever for weighing as shown in FIG.
11. A polystyrene bead with known mass was placed on the reference
cantilever arm to improve the resolution of the measurement, as
discussed above. The diatom and the reference bead were placed 2.8
.mu.m and 17.4 .mu.m away from the suspending end of the
cantilever, respectively. As a result, the differential resonance
frequency between two adjacent cantilevers was measured as 2173 Hz,
and the differential mass between the two particles was measured as
42.2 nano-gram with the mass of the diatom being 4.4 nano-gram.
[0050] In one aspect of the present disclosure, the resonator
includes a pair of arms cantilevered from a base, in which the base
is configured for engagement with an oscillator or shaker to induce
oscillation of the arms. Each arm defines a surface configured to
receive a micro- or nano-sized particle or object. The arms further
define interdigitating fingers between each other that are adapted
to define a diffraction pattern from incident light reflected from
the fingers as the cantilevered arms oscillate. In one method of
using the system, a target particle is mounted on a sensor arm,
while the other arm, or the reference arm, may be unloaded or
loaded with a particle having a known mass. The base of the
resonator is oscillated to cause vibration of the cantilevered
sensor and reference arms at their respective resonant frequencies.
The resonance frequencies of both arms are obtained by sensing the
intensity of a diffraction mode produced by the interdigitated
fingers. This approach prevents the user from having to perform two
different experiments (one for each cantilever) and allows
obtaining the two resonance frequencies in one experiment. Hence,
the differential frequency, or difference between the detected
resonant frequencies of the two arms, is also obtained by the same
way. The differential frequency value can be used in an equation to
solve for the mass of the target particle on the sensor arm.
Alternatively, the resonance frequencies observed experimentally
can be used in a finite element simulation to determine the mass of
the loaded particles.
[0051] With this versatile method it is possible to isolate
fragments of cells, individual cells, or individual groups of cells
such as prostate stem cell spheres, from culture and measure their
weight. The same system can be used to aggregate and measure the
humidity response of cells, such as spore cells, while minimizing
the effect of the humidity on the sensor itself due to the
inherently differential nature of the measurement. The system and
resonator disclosed herein provides capability of extracting and
weighing an individual particle, such as a diatom from a cluster of
micro-particles found in outdoors pond water.
[0052] Those skilled in the art will recognize that numerous
modifications can be made to the specific implementations described
above. The implementations should not be limited to the particular
limitations described. Other implementations may be possible.
* * * * *